Question

In the following exercises, simplify each expression using the properties for exponents.

$ⓐd^3·d^6ⓑ4^{5x}·4^{9x}ⓒ2y·4y^3ⓓw·w^2·w^3$

Short answer

The simplified form of given expression$d^3·d^6=d^9$

The simplified form of given expression$4^{5x}·4^{9x}=4^{14x}$

The simplified form of given expression$2y·4y^3=8y^4$

The simplified form of given expression$w·w^2·w^3=w^6$

Step-by-step solution

Step 1. Given Information 

In the given question we have to simplify the given expression:

$ⓐd^3·d^6ⓑ4^{5x}·4^{9x}ⓒ2y·4y^3ⓓw·w^2·w^3$

Part (a) Step 1. The given expression is d3·d6

Use the Product Property, $a^m·a^n=a^{m+n}$

$d^3·d^6=d^{6+3}$

Simplify.

$d^3·d^6=d^9$

Part (b) Step 1. The given expression is 45x·49x

Use the Product Property, $a^m·a^n=a^{m+n}$

$4^{5x}·4^{9x}=4^{5x+9x}$

Simplify.

$4^{5x}·4^{9x}=4^{14x}$

Part (c) Step 1. The given expression is 2y·4y3

$2y·4y^3=2y^1·4y^3$

$2y·4y^3=2·4·y^1·y^3$

Use the Product Property, $a^m·a^n=a^{m+n}$

$2y·4y^3=2·4·y^{3+1}$

Simplify.

$2y·4y^3=8y^4$

Part (d) Step 1. The given expression is w·w2·w3

$w·w^2·w^3=w^1·w^2·w^3$

Use the Product Property, $a^m·a^n=a^{m+n}$

$w·w^2·w^3=w^{1+2+3}$

Simplify.

role="math" localid="1644850947503" $w·w^2·w^3=w^6$